Properties

Label 1050.3.p.c.451.1
Level $1050$
Weight $3$
Character 1050.451
Analytic conductor $28.610$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.151613669376.6
Defining polynomial: \( x^{8} - 12x^{6} + 95x^{4} - 588x^{2} + 2401 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 451.1
Root \(2.56149 - 0.662382i\) of defining polynomial
Character \(\chi\) \(=\) 1050.451
Dual form 1050.3.p.c.901.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-0.440173 - 6.98615i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-0.440173 - 6.98615i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.76860 + 6.52741i) q^{11} +(3.00000 - 1.73205i) q^{12} -21.3906i q^{13} +(-8.24500 + 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(18.1757 + 10.4937i) q^{17} +(2.12132 - 3.67423i) q^{18} +(20.8728 - 12.0509i) q^{19} +(-5.38992 + 10.8604i) q^{21} +10.6592 q^{22} +(2.79005 + 4.83250i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-26.1981 + 15.1255i) q^{26} -5.19615i q^{27} +(12.5405 + 6.22374i) q^{28} -9.96625 q^{29} +(5.70073 + 3.29132i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(11.3058 - 6.52741i) q^{33} -29.6807i q^{34} -6.00000 q^{36} +(11.1983 + 19.3960i) q^{37} +(-29.5187 - 17.0426i) q^{38} +(-18.5248 + 32.0860i) q^{39} -51.0827i q^{41} +(17.1125 - 1.07820i) q^{42} -34.7656 q^{43} +(-7.53720 - 13.0548i) q^{44} +(3.94572 - 6.83419i) q^{46} +(67.2462 - 38.8246i) q^{47} +6.92820i q^{48} +(-48.6125 + 6.15023i) q^{49} +(-18.1757 - 31.4812i) q^{51} +(37.0497 + 21.3906i) q^{52} +(24.8989 - 43.1262i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} -41.7457 q^{57} +(7.04720 + 12.2061i) q^{58} +(72.9362 + 42.1098i) q^{59} +(-72.4404 + 41.8235i) q^{61} -9.30925i q^{62} +(17.4903 - 11.6228i) q^{63} +8.00000 q^{64} +(-15.9888 - 9.23115i) q^{66} +(33.2911 - 57.6618i) q^{67} +(-36.3513 + 20.9874i) q^{68} -9.66501i q^{69} -68.1049 q^{71} +(4.24264 + 7.34847i) q^{72} +(-75.9128 - 43.8283i) q^{73} +(15.8368 - 27.4301i) q^{74} +48.2038i q^{76} +(47.2603 + 23.4548i) q^{77} +52.3962 q^{78} +(-49.3730 - 85.5165i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-62.5632 + 36.1209i) q^{82} -26.9448i q^{83} +(-13.4209 - 20.1960i) q^{84} +(24.5830 + 42.5790i) q^{86} +(14.9494 + 8.63103i) q^{87} +(-10.6592 + 18.4623i) q^{88} +(12.0453 - 6.95436i) q^{89} +(-149.438 + 9.41559i) q^{91} -11.1602 q^{92} +(-5.70073 - 9.87395i) q^{93} +(-95.1005 - 54.9063i) q^{94} +(8.48528 - 4.89898i) q^{96} -3.69132i q^{97} +(41.9067 + 55.1890i) q^{98} -22.6116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} + 24 q^{12} - 16 q^{14} - 16 q^{16} - 24 q^{17} + 72 q^{19} + 24 q^{22} + 60 q^{23} - 72 q^{26} - 24 q^{29} + 96 q^{31} + 12 q^{33} - 48 q^{36} - 24 q^{37} - 180 q^{38} - 12 q^{39} + 12 q^{42} - 112 q^{43} - 8 q^{44} + 32 q^{46} + 84 q^{47} - 264 q^{49} + 24 q^{51} + 24 q^{52} + 44 q^{53} + 40 q^{56} - 144 q^{57} + 104 q^{58} + 312 q^{59} - 204 q^{61} + 64 q^{64} - 36 q^{66} + 120 q^{67} + 48 q^{68} - 64 q^{71} + 84 q^{73} - 16 q^{74} + 228 q^{77} + 144 q^{78} - 144 q^{79} - 36 q^{81} - 60 q^{82} + 176 q^{86} + 36 q^{87} - 24 q^{88} - 336 q^{89} - 296 q^{91} - 240 q^{92} - 96 q^{93} + 36 q^{94} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 1.22474i −0.353553 0.612372i
\(3\) −1.50000 0.866025i −0.500000 0.288675i
\(4\) −1.00000 + 1.73205i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) −0.440173 6.98615i −0.0628819 0.998021i
\(8\) 2.82843 0.353553
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −3.76860 + 6.52741i −0.342600 + 0.593401i −0.984915 0.173040i \(-0.944641\pi\)
0.642315 + 0.766441i \(0.277974\pi\)
\(12\) 3.00000 1.73205i 0.250000 0.144338i
\(13\) 21.3906i 1.64543i −0.568451 0.822717i \(-0.692457\pi\)
0.568451 0.822717i \(-0.307543\pi\)
\(14\) −8.24500 + 5.47905i −0.588928 + 0.391361i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) 18.1757 + 10.4937i 1.06916 + 0.617278i 0.927951 0.372703i \(-0.121569\pi\)
0.141205 + 0.989980i \(0.454902\pi\)
\(18\) 2.12132 3.67423i 0.117851 0.204124i
\(19\) 20.8728 12.0509i 1.09857 0.634260i 0.162726 0.986671i \(-0.447971\pi\)
0.935845 + 0.352411i \(0.114638\pi\)
\(20\) 0 0
\(21\) −5.38992 + 10.8604i −0.256663 + 0.517163i
\(22\) 10.6592 0.484510
\(23\) 2.79005 + 4.83250i 0.121306 + 0.210109i 0.920283 0.391253i \(-0.127958\pi\)
−0.798977 + 0.601362i \(0.794625\pi\)
\(24\) −4.24264 2.44949i −0.176777 0.102062i
\(25\) 0 0
\(26\) −26.1981 + 15.1255i −1.00762 + 0.581749i
\(27\) 5.19615i 0.192450i
\(28\) 12.5405 + 6.22374i 0.447876 + 0.222277i
\(29\) −9.96625 −0.343664 −0.171832 0.985126i \(-0.554969\pi\)
−0.171832 + 0.985126i \(0.554969\pi\)
\(30\) 0 0
\(31\) 5.70073 + 3.29132i 0.183894 + 0.106171i 0.589121 0.808045i \(-0.299474\pi\)
−0.405227 + 0.914216i \(0.632807\pi\)
\(32\) −2.82843 + 4.89898i −0.0883883 + 0.153093i
\(33\) 11.3058 6.52741i 0.342600 0.197800i
\(34\) 29.6807i 0.872962i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 11.1983 + 19.3960i 0.302656 + 0.524216i 0.976737 0.214442i \(-0.0687933\pi\)
−0.674080 + 0.738658i \(0.735460\pi\)
\(38\) −29.5187 17.0426i −0.776807 0.448490i
\(39\) −18.5248 + 32.0860i −0.474996 + 0.822717i
\(40\) 0 0
\(41\) 51.0827i 1.24592i −0.782254 0.622959i \(-0.785930\pi\)
0.782254 0.622959i \(-0.214070\pi\)
\(42\) 17.1125 1.07820i 0.407440 0.0256714i
\(43\) −34.7656 −0.808503 −0.404252 0.914648i \(-0.632468\pi\)
−0.404252 + 0.914648i \(0.632468\pi\)
\(44\) −7.53720 13.0548i −0.171300 0.296700i
\(45\) 0 0
\(46\) 3.94572 6.83419i 0.0857766 0.148569i
\(47\) 67.2462 38.8246i 1.43077 0.826056i 0.433591 0.901110i \(-0.357246\pi\)
0.997179 + 0.0750536i \(0.0239128\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −48.6125 + 6.15023i −0.992092 + 0.125515i
\(50\) 0 0
\(51\) −18.1757 31.4812i −0.356385 0.617278i
\(52\) 37.0497 + 21.3906i 0.712494 + 0.411359i
\(53\) 24.8989 43.1262i 0.469791 0.813703i −0.529612 0.848240i \(-0.677662\pi\)
0.999403 + 0.0345374i \(0.0109958\pi\)
\(54\) −6.36396 + 3.67423i −0.117851 + 0.0680414i
\(55\) 0 0
\(56\) −1.24500 19.7598i −0.0222321 0.352854i
\(57\) −41.7457 −0.732381
\(58\) 7.04720 + 12.2061i 0.121504 + 0.210450i
\(59\) 72.9362 + 42.1098i 1.23621 + 0.713725i 0.968317 0.249725i \(-0.0803401\pi\)
0.267890 + 0.963449i \(0.413673\pi\)
\(60\) 0 0
\(61\) −72.4404 + 41.8235i −1.18755 + 0.685631i −0.957749 0.287607i \(-0.907140\pi\)
−0.229799 + 0.973238i \(0.573807\pi\)
\(62\) 9.30925i 0.150149i
\(63\) 17.4903 11.6228i 0.277624 0.184489i
\(64\) 8.00000 0.125000
\(65\) 0 0
\(66\) −15.9888 9.23115i −0.242255 0.139866i
\(67\) 33.2911 57.6618i 0.496882 0.860625i −0.503112 0.864221i \(-0.667812\pi\)
0.999994 + 0.00359682i \(0.00114491\pi\)
\(68\) −36.3513 + 20.9874i −0.534578 + 0.308639i
\(69\) 9.66501i 0.140073i
\(70\) 0 0
\(71\) −68.1049 −0.959224 −0.479612 0.877481i \(-0.659223\pi\)
−0.479612 + 0.877481i \(0.659223\pi\)
\(72\) 4.24264 + 7.34847i 0.0589256 + 0.102062i
\(73\) −75.9128 43.8283i −1.03990 0.600387i −0.120096 0.992762i \(-0.538320\pi\)
−0.919805 + 0.392375i \(0.871654\pi\)
\(74\) 15.8368 27.4301i 0.214010 0.370677i
\(75\) 0 0
\(76\) 48.2038i 0.634260i
\(77\) 47.2603 + 23.4548i 0.613770 + 0.304608i
\(78\) 52.3962 0.671746
\(79\) −49.3730 85.5165i −0.624974 1.08249i −0.988546 0.150921i \(-0.951776\pi\)
0.363572 0.931566i \(-0.381557\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) −62.5632 + 36.1209i −0.762966 + 0.440499i
\(83\) 26.9448i 0.324636i −0.986739 0.162318i \(-0.948103\pi\)
0.986739 0.162318i \(-0.0518970\pi\)
\(84\) −13.4209 20.1960i −0.159772 0.240429i
\(85\) 0 0
\(86\) 24.5830 + 42.5790i 0.285849 + 0.495105i
\(87\) 14.9494 + 8.63103i 0.171832 + 0.0992072i
\(88\) −10.6592 + 18.4623i −0.121127 + 0.209799i
\(89\) 12.0453 6.95436i 0.135341 0.0781389i −0.430801 0.902447i \(-0.641769\pi\)
0.566142 + 0.824308i \(0.308436\pi\)
\(90\) 0 0
\(91\) −149.438 + 9.41559i −1.64218 + 0.103468i
\(92\) −11.1602 −0.121306
\(93\) −5.70073 9.87395i −0.0612981 0.106171i
\(94\) −95.1005 54.9063i −1.01171 0.584110i
\(95\) 0 0
\(96\) 8.48528 4.89898i 0.0883883 0.0510310i
\(97\) 3.69132i 0.0380549i −0.999819 0.0190274i \(-0.993943\pi\)
0.999819 0.0190274i \(-0.00605698\pi\)
\(98\) 41.9067 + 55.1890i 0.427619 + 0.563153i
\(99\) −22.6116 −0.228400
\(100\) 0 0
\(101\) −158.170 91.3195i −1.56604 0.904154i −0.996624 0.0821041i \(-0.973836\pi\)
−0.569416 0.822049i \(-0.692831\pi\)
\(102\) −25.7043 + 44.5211i −0.252003 + 0.436481i
\(103\) −78.8521 + 45.5253i −0.765555 + 0.441993i −0.831287 0.555844i \(-0.812395\pi\)
0.0657318 + 0.997837i \(0.479062\pi\)
\(104\) 60.5019i 0.581749i
\(105\) 0 0
\(106\) −70.4249 −0.664385
\(107\) −25.7682 44.6318i −0.240824 0.417120i 0.720125 0.693844i \(-0.244084\pi\)
−0.960949 + 0.276724i \(0.910751\pi\)
\(108\) 9.00000 + 5.19615i 0.0833333 + 0.0481125i
\(109\) −19.1807 + 33.2219i −0.175970 + 0.304788i −0.940496 0.339804i \(-0.889639\pi\)
0.764527 + 0.644592i \(0.222973\pi\)
\(110\) 0 0
\(111\) 38.7920i 0.349477i
\(112\) −23.3204 + 15.4971i −0.208218 + 0.138367i
\(113\) −198.558 −1.75715 −0.878573 0.477608i \(-0.841504\pi\)
−0.878573 + 0.477608i \(0.841504\pi\)
\(114\) 29.5187 + 51.1278i 0.258936 + 0.448490i
\(115\) 0 0
\(116\) 9.96625 17.2621i 0.0859160 0.148811i
\(117\) 55.5745 32.0860i 0.474996 0.274239i
\(118\) 119.104i 1.00936i
\(119\) 65.3102 131.597i 0.548825 1.10586i
\(120\) 0 0
\(121\) 32.0953 + 55.5907i 0.265250 + 0.459427i
\(122\) 102.446 + 59.1474i 0.839723 + 0.484814i
\(123\) −44.2389 + 76.6240i −0.359666 + 0.622959i
\(124\) −11.4015 + 6.58263i −0.0919472 + 0.0530857i
\(125\) 0 0
\(126\) −26.6025 13.2026i −0.211131 0.104782i
\(127\) −74.1132 −0.583569 −0.291784 0.956484i \(-0.594249\pi\)
−0.291784 + 0.956484i \(0.594249\pi\)
\(128\) −5.65685 9.79796i −0.0441942 0.0765466i
\(129\) 52.1485 + 30.1079i 0.404252 + 0.233395i
\(130\) 0 0
\(131\) 17.3500 10.0170i 0.132443 0.0764657i −0.432315 0.901723i \(-0.642303\pi\)
0.564757 + 0.825257i \(0.308970\pi\)
\(132\) 26.1096i 0.197800i
\(133\) −93.3773 140.516i −0.702085 1.05651i
\(134\) −94.1614 −0.702697
\(135\) 0 0
\(136\) 51.4085 + 29.6807i 0.378004 + 0.218241i
\(137\) 43.0853 74.6259i 0.314491 0.544715i −0.664838 0.746988i \(-0.731499\pi\)
0.979329 + 0.202273i \(0.0648328\pi\)
\(138\) −11.8372 + 6.83419i −0.0857766 + 0.0495231i
\(139\) 232.502i 1.67268i 0.548213 + 0.836339i \(0.315308\pi\)
−0.548213 + 0.836339i \(0.684692\pi\)
\(140\) 0 0
\(141\) −134.492 −0.953847
\(142\) 48.1574 + 83.4111i 0.339137 + 0.587402i
\(143\) 139.625 + 80.6128i 0.976402 + 0.563726i
\(144\) 6.00000 10.3923i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) 123.965i 0.849076i
\(147\) 78.2450 + 32.8743i 0.532279 + 0.223635i
\(148\) −44.7931 −0.302656
\(149\) 109.963 + 190.462i 0.738008 + 1.27827i 0.953391 + 0.301738i \(0.0975666\pi\)
−0.215383 + 0.976530i \(0.569100\pi\)
\(150\) 0 0
\(151\) 130.461 225.965i 0.863980 1.49646i −0.00407633 0.999992i \(-0.501298\pi\)
0.868056 0.496466i \(-0.165369\pi\)
\(152\) 59.0373 34.0852i 0.388403 0.224245i
\(153\) 62.9623i 0.411518i
\(154\) −4.69190 74.4668i −0.0304669 0.483551i
\(155\) 0 0
\(156\) −37.0497 64.1719i −0.237498 0.411359i
\(157\) −98.8921 57.0954i −0.629886 0.363665i 0.150822 0.988561i \(-0.451808\pi\)
−0.780708 + 0.624896i \(0.785141\pi\)
\(158\) −69.8239 + 120.939i −0.441923 + 0.765434i
\(159\) −74.6968 + 43.1262i −0.469791 + 0.271234i
\(160\) 0 0
\(161\) 32.5325 21.6188i 0.202065 0.134278i
\(162\) 12.7279 0.0785674
\(163\) −24.3581 42.1894i −0.149436 0.258831i 0.781583 0.623801i \(-0.214412\pi\)
−0.931019 + 0.364970i \(0.881079\pi\)
\(164\) 88.4777 + 51.0827i 0.539498 + 0.311480i
\(165\) 0 0
\(166\) −33.0005 + 19.0528i −0.198798 + 0.114776i
\(167\) 49.6127i 0.297082i 0.988906 + 0.148541i \(0.0474577\pi\)
−0.988906 + 0.148541i \(0.952542\pi\)
\(168\) −15.2450 + 30.7179i −0.0907440 + 0.182845i
\(169\) −288.560 −1.70745
\(170\) 0 0
\(171\) 62.6185 + 36.1528i 0.366190 + 0.211420i
\(172\) 34.7656 60.2159i 0.202126 0.350092i
\(173\) −203.811 + 117.670i −1.17810 + 0.680176i −0.955574 0.294751i \(-0.904763\pi\)
−0.222525 + 0.974927i \(0.571430\pi\)
\(174\) 24.4122i 0.140300i
\(175\) 0 0
\(176\) 30.1488 0.171300
\(177\) −72.9362 126.329i −0.412069 0.713725i
\(178\) −17.0346 9.83495i −0.0957002 0.0552525i
\(179\) 22.1049 38.2868i 0.123491 0.213893i −0.797651 0.603119i \(-0.793924\pi\)
0.921142 + 0.389226i \(0.127258\pi\)
\(180\) 0 0
\(181\) 117.049i 0.646679i 0.946283 + 0.323340i \(0.104806\pi\)
−0.946283 + 0.323340i \(0.895194\pi\)
\(182\) 117.200 + 176.366i 0.643958 + 0.969043i
\(183\) 144.881 0.791699
\(184\) 7.89145 + 13.6684i 0.0428883 + 0.0742847i
\(185\) 0 0
\(186\) −8.06204 + 13.9639i −0.0433443 + 0.0750746i
\(187\) −136.994 + 79.0933i −0.732586 + 0.422959i
\(188\) 155.299i 0.826056i
\(189\) −36.3011 + 2.28721i −0.192069 + 0.0121016i
\(190\) 0 0
\(191\) −117.156 202.920i −0.613383 1.06241i −0.990666 0.136313i \(-0.956475\pi\)
0.377283 0.926098i \(-0.376858\pi\)
\(192\) −12.0000 6.92820i −0.0625000 0.0360844i
\(193\) 9.78252 16.9438i 0.0506866 0.0877918i −0.839569 0.543253i \(-0.817192\pi\)
0.890256 + 0.455461i \(0.150526\pi\)
\(194\) −4.52093 + 2.61016i −0.0233037 + 0.0134544i
\(195\) 0 0
\(196\) 37.9600 90.3495i 0.193673 0.460967i
\(197\) −179.443 −0.910877 −0.455438 0.890267i \(-0.650517\pi\)
−0.455438 + 0.890267i \(0.650517\pi\)
\(198\) 15.9888 + 27.6934i 0.0807516 + 0.139866i
\(199\) −221.630 127.958i −1.11372 0.643006i −0.173928 0.984758i \(-0.555646\pi\)
−0.939790 + 0.341753i \(0.888979\pi\)
\(200\) 0 0
\(201\) −99.8732 + 57.6618i −0.496882 + 0.286875i
\(202\) 258.291i 1.27867i
\(203\) 4.38688 + 69.6257i 0.0216102 + 0.342984i
\(204\) 72.7026 0.356385
\(205\) 0 0
\(206\) 111.514 + 64.3825i 0.541329 + 0.312536i
\(207\) −8.37014 + 14.4975i −0.0404355 + 0.0700363i
\(208\) −74.0994 + 42.7813i −0.356247 + 0.205679i
\(209\) 181.661i 0.869190i
\(210\) 0 0
\(211\) 196.891 0.933132 0.466566 0.884486i \(-0.345491\pi\)
0.466566 + 0.884486i \(0.345491\pi\)
\(212\) 49.7979 + 86.2525i 0.234896 + 0.406851i
\(213\) 102.157 + 58.9806i 0.479612 + 0.276904i
\(214\) −36.4417 + 63.1189i −0.170288 + 0.294948i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) 20.4843 41.2749i 0.0943977 0.190207i
\(218\) 54.2512 0.248859
\(219\) 75.9128 + 131.485i 0.346634 + 0.600387i
\(220\) 0 0
\(221\) 224.467 388.789i 1.01569 1.75923i
\(222\) −47.5103 + 27.4301i −0.214010 + 0.123559i
\(223\) 431.015i 1.93280i −0.257039 0.966401i \(-0.582747\pi\)
0.257039 0.966401i \(-0.417253\pi\)
\(224\) 35.4700 + 17.6034i 0.158348 + 0.0785866i
\(225\) 0 0
\(226\) 140.401 + 243.182i 0.621245 + 1.07603i
\(227\) 151.637 + 87.5479i 0.668006 + 0.385673i 0.795321 0.606189i \(-0.207302\pi\)
−0.127315 + 0.991862i \(0.540636\pi\)
\(228\) 41.7457 72.3057i 0.183095 0.317130i
\(229\) 29.0717 16.7846i 0.126951 0.0732951i −0.435180 0.900344i \(-0.643315\pi\)
0.562131 + 0.827048i \(0.309982\pi\)
\(230\) 0 0
\(231\) −50.5779 76.1108i −0.218952 0.329484i
\(232\) −28.1888 −0.121504
\(233\) 77.4567 + 134.159i 0.332432 + 0.575790i 0.982988 0.183669i \(-0.0587973\pi\)
−0.650556 + 0.759458i \(0.725464\pi\)
\(234\) −78.5942 45.3764i −0.335873 0.193916i
\(235\) 0 0
\(236\) −145.872 + 84.2195i −0.618104 + 0.356862i
\(237\) 171.033i 0.721658i
\(238\) −207.354 + 13.0647i −0.871235 + 0.0548935i
\(239\) 316.591 1.32465 0.662325 0.749217i \(-0.269570\pi\)
0.662325 + 0.749217i \(0.269570\pi\)
\(240\) 0 0
\(241\) 202.219 + 116.751i 0.839084 + 0.484446i 0.856953 0.515395i \(-0.172355\pi\)
−0.0178685 + 0.999840i \(0.505688\pi\)
\(242\) 45.3896 78.6171i 0.187560 0.324864i
\(243\) 13.5000 7.79423i 0.0555556 0.0320750i
\(244\) 167.294i 0.685631i
\(245\) 0 0
\(246\) 125.126 0.508644
\(247\) −257.777 446.484i −1.04363 1.80763i
\(248\) 16.1241 + 9.30925i 0.0650165 + 0.0375373i
\(249\) −23.3349 + 40.4172i −0.0937143 + 0.162318i
\(250\) 0 0
\(251\) 56.6879i 0.225848i −0.993604 0.112924i \(-0.963978\pi\)
0.993604 0.112924i \(-0.0360217\pi\)
\(252\) 2.64104 + 41.9169i 0.0104803 + 0.166337i
\(253\) −42.0583 −0.166238
\(254\) 52.4060 + 90.7698i 0.206323 + 0.357361i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 251.528 145.219i 0.978706 0.565056i 0.0768270 0.997044i \(-0.475521\pi\)
0.901879 + 0.431988i \(0.142188\pi\)
\(258\) 85.1581i 0.330070i
\(259\) 130.574 86.7704i 0.504147 0.335021i
\(260\) 0 0
\(261\) −14.9494 25.8931i −0.0572773 0.0992072i
\(262\) −24.5366 14.1662i −0.0936510 0.0540694i
\(263\) 222.298 385.031i 0.845238 1.46399i −0.0401768 0.999193i \(-0.512792\pi\)
0.885415 0.464802i \(-0.153875\pi\)
\(264\) 31.9776 18.4623i 0.121127 0.0699329i
\(265\) 0 0
\(266\) −106.069 + 213.723i −0.398755 + 0.803471i
\(267\) −24.0906 −0.0902270
\(268\) 66.5822 + 115.324i 0.248441 + 0.430312i
\(269\) −144.956 83.6902i −0.538869 0.311116i 0.205752 0.978604i \(-0.434036\pi\)
−0.744620 + 0.667488i \(0.767369\pi\)
\(270\) 0 0
\(271\) 2.24099 1.29384i 0.00826933 0.00477430i −0.495860 0.868403i \(-0.665147\pi\)
0.504129 + 0.863628i \(0.331814\pi\)
\(272\) 83.9498i 0.308639i
\(273\) 232.311 + 115.294i 0.850957 + 0.422322i
\(274\) −121.864 −0.444758
\(275\) 0 0
\(276\) 16.7403 + 9.66501i 0.0606532 + 0.0350181i
\(277\) 254.556 440.903i 0.918973 1.59171i 0.117996 0.993014i \(-0.462353\pi\)
0.800978 0.598694i \(-0.204314\pi\)
\(278\) 284.756 164.404i 1.02430 0.591381i
\(279\) 19.7479i 0.0707810i
\(280\) 0 0
\(281\) 210.688 0.749779 0.374890 0.927069i \(-0.377681\pi\)
0.374890 + 0.927069i \(0.377681\pi\)
\(282\) 95.1005 + 164.719i 0.337236 + 0.584110i
\(283\) 34.1964 + 19.7433i 0.120835 + 0.0697643i 0.559199 0.829033i \(-0.311109\pi\)
−0.438364 + 0.898797i \(0.644442\pi\)
\(284\) 68.1049 117.961i 0.239806 0.415356i
\(285\) 0 0
\(286\) 228.007i 0.797229i
\(287\) −356.871 + 22.4852i −1.24345 + 0.0783457i
\(288\) −16.9706 −0.0589256
\(289\) 75.7363 + 131.179i 0.262063 + 0.453907i
\(290\) 0 0
\(291\) −3.19678 + 5.53698i −0.0109855 + 0.0190274i
\(292\) 151.826 87.6565i 0.519951 0.300194i
\(293\) 89.6023i 0.305810i −0.988241 0.152905i \(-0.951137\pi\)
0.988241 0.152905i \(-0.0488628\pi\)
\(294\) −15.0649 119.076i −0.0512412 0.405020i
\(295\) 0 0
\(296\) 31.6735 + 54.8602i 0.107005 + 0.185338i
\(297\) 33.9174 + 19.5822i 0.114200 + 0.0659334i
\(298\) 155.511 269.354i 0.521850 0.903871i
\(299\) 103.370 59.6809i 0.345720 0.199602i
\(300\) 0 0
\(301\) 15.3029 + 242.878i 0.0508402 + 0.806903i
\(302\) −368.999 −1.22185
\(303\) 158.170 + 273.959i 0.522013 + 0.904154i
\(304\) −83.4914 48.2038i −0.274643 0.158565i
\(305\) 0 0
\(306\) 77.1128 44.5211i 0.252003 0.145494i
\(307\) 470.478i 1.53250i −0.642542 0.766251i \(-0.722120\pi\)
0.642542 0.766251i \(-0.277880\pi\)
\(308\) −87.8852 + 58.4024i −0.285341 + 0.189618i
\(309\) 157.704 0.510370
\(310\) 0 0
\(311\) 217.631 + 125.649i 0.699778 + 0.404017i 0.807265 0.590189i \(-0.200947\pi\)
−0.107487 + 0.994207i \(0.534280\pi\)
\(312\) −52.3962 + 90.7528i −0.167936 + 0.290874i
\(313\) −336.417 + 194.231i −1.07482 + 0.620545i −0.929493 0.368839i \(-0.879755\pi\)
−0.145322 + 0.989384i \(0.546422\pi\)
\(314\) 161.490i 0.514300i
\(315\) 0 0
\(316\) 197.492 0.624974
\(317\) −74.6898 129.366i −0.235614 0.408096i 0.723837 0.689971i \(-0.242377\pi\)
−0.959451 + 0.281875i \(0.909044\pi\)
\(318\) 105.637 + 60.9897i 0.332193 + 0.191792i
\(319\) 37.5588 65.0538i 0.117739 0.203930i
\(320\) 0 0
\(321\) 89.2636i 0.278080i
\(322\) −49.4815 24.5572i −0.153669 0.0762645i
\(323\) 505.837 1.56606
\(324\) −9.00000 15.5885i −0.0277778 0.0481125i
\(325\) 0 0
\(326\) −34.4475 + 59.6648i −0.105667 + 0.183021i
\(327\) 57.5420 33.2219i 0.175970 0.101596i
\(328\) 144.484i 0.440499i
\(329\) −300.835 452.702i −0.914391 1.37600i
\(330\) 0 0
\(331\) 235.465 + 407.838i 0.711375 + 1.23214i 0.964341 + 0.264663i \(0.0852607\pi\)
−0.252966 + 0.967475i \(0.581406\pi\)
\(332\) 46.6697 + 26.9448i 0.140571 + 0.0811590i
\(333\) −33.5948 + 58.1880i −0.100885 + 0.174739i
\(334\) 60.7628 35.0814i 0.181925 0.105034i
\(335\) 0 0
\(336\) 48.4014 3.04961i 0.144052 0.00907622i
\(337\) −532.478 −1.58005 −0.790027 0.613072i \(-0.789934\pi\)
−0.790027 + 0.613072i \(0.789934\pi\)
\(338\) 204.042 + 353.412i 0.603676 + 1.04560i
\(339\) 297.836 + 171.956i 0.878573 + 0.507244i
\(340\) 0 0
\(341\) −42.9675 + 24.8073i −0.126004 + 0.0727487i
\(342\) 102.256i 0.298993i
\(343\) 64.3643 + 336.907i 0.187651 + 0.982236i
\(344\) −98.3321 −0.285849
\(345\) 0 0
\(346\) 288.232 + 166.411i 0.833042 + 0.480957i
\(347\) −224.812 + 389.385i −0.647872 + 1.12215i 0.335758 + 0.941948i \(0.391008\pi\)
−0.983630 + 0.180199i \(0.942326\pi\)
\(348\) −29.8988 + 17.2621i −0.0859160 + 0.0496036i
\(349\) 330.676i 0.947495i −0.880661 0.473747i \(-0.842901\pi\)
0.880661 0.473747i \(-0.157099\pi\)
\(350\) 0 0
\(351\) −111.149 −0.316664
\(352\) −21.3184 36.9246i −0.0605637 0.104899i
\(353\) 235.014 + 135.686i 0.665763 + 0.384379i 0.794469 0.607304i \(-0.207749\pi\)
−0.128706 + 0.991683i \(0.541082\pi\)
\(354\) −103.147 + 178.657i −0.291377 + 0.504680i
\(355\) 0 0
\(356\) 27.8174i 0.0781389i
\(357\) −211.932 + 140.835i −0.593646 + 0.394496i
\(358\) −62.5221 −0.174643
\(359\) 3.79200 + 6.56794i 0.0105627 + 0.0182951i 0.871258 0.490825i \(-0.163304\pi\)
−0.860696 + 0.509120i \(0.829971\pi\)
\(360\) 0 0
\(361\) 109.950 190.440i 0.304572 0.527534i
\(362\) 143.355 82.7661i 0.396009 0.228636i
\(363\) 111.181i 0.306285i
\(364\) 133.130 268.250i 0.365741 0.736951i
\(365\) 0 0
\(366\) −102.446 177.442i −0.279908 0.484814i
\(367\) 460.216 + 265.706i 1.25400 + 0.723995i 0.971901 0.235392i \(-0.0756373\pi\)
0.282095 + 0.959386i \(0.408971\pi\)
\(368\) 11.1602 19.3300i 0.0303266 0.0525272i
\(369\) 132.717 76.6240i 0.359666 0.207653i
\(370\) 0 0
\(371\) −312.246 154.965i −0.841634 0.417695i
\(372\) 22.8029 0.0612981
\(373\) −287.484 497.937i −0.770734 1.33495i −0.937161 0.348897i \(-0.886556\pi\)
0.166427 0.986054i \(-0.446777\pi\)
\(374\) 193.738 + 111.855i 0.518016 + 0.299077i
\(375\) 0 0
\(376\) 190.201 109.813i 0.505854 0.292055i
\(377\) 213.185i 0.565476i
\(378\) 28.4700 + 42.8423i 0.0753174 + 0.113339i
\(379\) 627.464 1.65558 0.827789 0.561040i \(-0.189598\pi\)
0.827789 + 0.561040i \(0.189598\pi\)
\(380\) 0 0
\(381\) 111.170 + 64.1839i 0.291784 + 0.168462i
\(382\) −165.684 + 286.973i −0.433727 + 0.751238i
\(383\) 57.6870 33.3056i 0.150619 0.0869597i −0.422797 0.906225i \(-0.638952\pi\)
0.573415 + 0.819265i \(0.305618\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −27.6691 −0.0716817
\(387\) −52.1485 90.3238i −0.134751 0.233395i
\(388\) 6.39356 + 3.69132i 0.0164782 + 0.00951372i
\(389\) −274.525 + 475.491i −0.705719 + 1.22234i 0.260713 + 0.965416i \(0.416043\pi\)
−0.966431 + 0.256925i \(0.917291\pi\)
\(390\) 0 0
\(391\) 117.112i 0.299519i
\(392\) −137.497 + 17.3955i −0.350757 + 0.0443762i
\(393\) −34.7000 −0.0882950
\(394\) 126.885 + 219.772i 0.322044 + 0.557796i
\(395\) 0 0
\(396\) 22.6116 39.1644i 0.0571000 0.0989001i
\(397\) −449.091 + 259.283i −1.13121 + 0.653106i −0.944240 0.329259i \(-0.893201\pi\)
−0.186973 + 0.982365i \(0.559868\pi\)
\(398\) 361.920i 0.909347i
\(399\) 18.3753 + 291.642i 0.0460535 + 0.730931i
\(400\) 0 0
\(401\) 238.149 + 412.486i 0.593888 + 1.02864i 0.993703 + 0.112048i \(0.0357411\pi\)
−0.399815 + 0.916596i \(0.630926\pi\)
\(402\) 141.242 + 81.5462i 0.351349 + 0.202851i
\(403\) 70.4033 121.942i 0.174698 0.302586i
\(404\) 316.340 182.639i 0.783020 0.452077i
\(405\) 0 0
\(406\) 82.1717 54.6056i 0.202393 0.134497i
\(407\) −168.807 −0.414760
\(408\) −51.4085 89.0422i −0.126001 0.218241i
\(409\) −93.2552 53.8409i −0.228008 0.131640i 0.381645 0.924309i \(-0.375358\pi\)
−0.609653 + 0.792669i \(0.708691\pi\)
\(410\) 0 0
\(411\) −129.256 + 74.6259i −0.314491 + 0.181572i
\(412\) 182.101i 0.441993i
\(413\) 262.080 528.079i 0.634577 1.27864i
\(414\) 23.6743 0.0571844
\(415\) 0 0
\(416\) 104.792 + 60.5019i 0.251905 + 0.145437i
\(417\) 201.353 348.753i 0.482861 0.836339i
\(418\) 222.488 128.454i 0.532268 0.307305i
\(419\) 323.811i 0.772818i 0.922328 + 0.386409i \(0.126285\pi\)
−0.922328 + 0.386409i \(0.873715\pi\)
\(420\) 0 0
\(421\) −238.957 −0.567595 −0.283797 0.958884i \(-0.591594\pi\)
−0.283797 + 0.958884i \(0.591594\pi\)
\(422\) −139.223 241.141i −0.329912 0.571424i
\(423\) 201.739 + 116.474i 0.476924 + 0.275352i
\(424\) 70.4249 121.979i 0.166096 0.287687i
\(425\) 0 0
\(426\) 166.822i 0.391601i
\(427\) 324.071 + 487.670i 0.758950 + 1.14208i
\(428\) 103.073 0.240824
\(429\) −139.625 241.838i −0.325467 0.563726i
\(430\) 0 0
\(431\) 95.8960 166.097i 0.222497 0.385375i −0.733069 0.680154i \(-0.761913\pi\)
0.955565 + 0.294779i \(0.0952461\pi\)
\(432\) −18.0000 + 10.3923i −0.0416667 + 0.0240563i
\(433\) 122.083i 0.281946i −0.990013 0.140973i \(-0.954977\pi\)
0.990013 0.140973i \(-0.0450231\pi\)
\(434\) −65.0358 + 4.09768i −0.149852 + 0.00944166i
\(435\) 0 0
\(436\) −38.3614 66.4438i −0.0879848 0.152394i
\(437\) 116.472 + 67.2454i 0.266527 + 0.153880i
\(438\) 107.357 185.948i 0.245107 0.424538i
\(439\) −217.656 + 125.664i −0.495800 + 0.286250i −0.726978 0.686661i \(-0.759076\pi\)
0.231177 + 0.972912i \(0.425742\pi\)
\(440\) 0 0
\(441\) −88.8975 117.074i −0.201582 0.265473i
\(442\) −634.890 −1.43640
\(443\) 54.8946 + 95.0802i 0.123916 + 0.214628i 0.921309 0.388832i \(-0.127121\pi\)
−0.797393 + 0.603460i \(0.793788\pi\)
\(444\) 67.1897 + 38.7920i 0.151328 + 0.0873693i
\(445\) 0 0
\(446\) −527.883 + 304.773i −1.18359 + 0.683349i
\(447\) 380.924i 0.852178i
\(448\) −3.52139 55.8892i −0.00786024 0.124753i
\(449\) 806.490 1.79619 0.898095 0.439801i \(-0.144951\pi\)
0.898095 + 0.439801i \(0.144951\pi\)
\(450\) 0 0
\(451\) 333.437 + 192.510i 0.739329 + 0.426852i
\(452\) 198.558 343.912i 0.439287 0.760867i
\(453\) −391.383 + 225.965i −0.863980 + 0.498819i
\(454\) 247.623i 0.545425i
\(455\) 0 0
\(456\) −118.075 −0.258936
\(457\) −386.226 668.964i −0.845135 1.46382i −0.885504 0.464631i \(-0.846187\pi\)
0.0403698 0.999185i \(-0.487146\pi\)
\(458\) −41.1137 23.7370i −0.0897678 0.0518275i
\(459\) 54.5270 94.4435i 0.118795 0.205759i
\(460\) 0 0
\(461\) 793.611i 1.72150i −0.509029 0.860749i \(-0.669995\pi\)
0.509029 0.860749i \(-0.330005\pi\)
\(462\) −57.4523 + 115.764i −0.124356 + 0.250570i
\(463\) 274.227 0.592284 0.296142 0.955144i \(-0.404300\pi\)
0.296142 + 0.955144i \(0.404300\pi\)
\(464\) 19.9325 + 34.5241i 0.0429580 + 0.0744054i
\(465\) 0 0
\(466\) 109.540 189.730i 0.235065 0.407145i
\(467\) −344.357 + 198.815i −0.737381 + 0.425727i −0.821116 0.570761i \(-0.806648\pi\)
0.0837354 + 0.996488i \(0.473315\pi\)
\(468\) 128.344i 0.274239i
\(469\) −417.488 207.195i −0.890166 0.441781i
\(470\) 0 0
\(471\) 98.8921 + 171.286i 0.209962 + 0.363665i
\(472\) 206.295 + 119.104i 0.437065 + 0.252340i
\(473\) 131.018 226.930i 0.276993 0.479766i
\(474\) 209.472 120.939i 0.441923 0.255145i
\(475\) 0 0
\(476\) 162.622 + 244.717i 0.341643 + 0.514112i
\(477\) 149.394 0.313194
\(478\) −223.864 387.743i −0.468334 0.811179i
\(479\) −165.573 95.5938i −0.345665 0.199570i 0.317110 0.948389i \(-0.397288\pi\)
−0.662774 + 0.748819i \(0.730621\pi\)
\(480\) 0 0
\(481\) 414.893 239.538i 0.862563 0.498001i
\(482\) 330.223i 0.685110i
\(483\) −67.5212 + 4.25428i −0.139795 + 0.00880803i
\(484\) −128.381 −0.265250
\(485\) 0 0
\(486\) −19.0919 11.0227i −0.0392837 0.0226805i
\(487\) −95.0092 + 164.561i −0.195091 + 0.337907i −0.946930 0.321439i \(-0.895833\pi\)
0.751840 + 0.659346i \(0.229167\pi\)
\(488\) −204.892 + 118.295i −0.419862 + 0.242407i
\(489\) 84.3788i 0.172554i
\(490\) 0 0
\(491\) −211.384 −0.430517 −0.215258 0.976557i \(-0.569059\pi\)
−0.215258 + 0.976557i \(0.569059\pi\)
\(492\) −88.4777 153.248i −0.179833 0.311480i
\(493\) −181.143 104.583i −0.367430 0.212136i
\(494\) −364.552 + 631.423i −0.737960 + 1.27818i
\(495\) 0 0
\(496\) 26.3305i 0.0530857i
\(497\) 29.9779 + 475.791i 0.0603178 + 0.957325i
\(498\) 66.0010 0.132532
\(499\) 126.864 + 219.734i 0.254236 + 0.440349i 0.964688 0.263396i \(-0.0848427\pi\)
−0.710452 + 0.703746i \(0.751509\pi\)
\(500\) 0 0
\(501\) 42.9658 74.4190i 0.0857601 0.148541i
\(502\) −69.4282 + 40.0844i −0.138303 + 0.0798494i
\(503\) 217.815i 0.433033i 0.976279 + 0.216516i \(0.0694695\pi\)
−0.976279 + 0.216516i \(0.930531\pi\)
\(504\) 49.4700 32.8743i 0.0981547 0.0652268i
\(505\) 0 0
\(506\) 29.7397 + 51.5107i 0.0587741 + 0.101800i
\(507\) 432.839 + 249.900i 0.853727 + 0.492899i
\(508\) 74.1132 128.368i 0.145892 0.252693i
\(509\) −24.6582 + 14.2364i −0.0484444 + 0.0279694i −0.524027 0.851702i \(-0.675571\pi\)
0.475582 + 0.879671i \(0.342237\pi\)
\(510\) 0 0
\(511\) −272.776 + 549.630i −0.533808 + 1.07560i
\(512\) 22.6274 0.0441942
\(513\) −62.6185 108.458i −0.122063 0.211420i
\(514\) −355.714 205.371i −0.692050 0.399555i
\(515\) 0 0
\(516\) −104.297 + 60.2159i −0.202126 + 0.116697i
\(517\) 585.258i 1.13203i
\(518\) −198.601 98.5640i −0.383400 0.190278i
\(519\) 407.622 0.785399
\(520\) 0 0
\(521\) 671.401 + 387.634i 1.28868 + 0.744019i 0.978418 0.206633i \(-0.0662507\pi\)
0.310260 + 0.950652i \(0.399584\pi\)
\(522\) −21.1416 + 36.6184i −0.0405012 + 0.0701501i
\(523\) 88.7388 51.2334i 0.169673 0.0979605i −0.412759 0.910840i \(-0.635435\pi\)
0.582431 + 0.812880i \(0.302101\pi\)
\(524\) 40.0681i 0.0764657i
\(525\) 0 0
\(526\) −628.752 −1.19535
\(527\) 69.0763 + 119.644i 0.131075 + 0.227028i
\(528\) −45.2232 26.1096i −0.0856500 0.0494501i
\(529\) 248.931 431.162i 0.470570 0.815050i
\(530\) 0 0
\(531\) 252.659i 0.475816i
\(532\) 336.759 21.2180i 0.633005 0.0398835i
\(533\) −1092.69 −2.05008
\(534\) 17.0346 + 29.5049i 0.0319001 + 0.0552525i
\(535\) 0 0
\(536\) 94.1614 163.092i 0.175674 0.304277i
\(537\) −66.3147 + 38.2868i −0.123491 + 0.0712976i
\(538\) 236.712i 0.439984i
\(539\) 143.056 340.491i 0.265410 0.631709i
\(540\) 0 0
\(541\) 408.868 + 708.180i 0.755763 + 1.30902i 0.944994 + 0.327088i \(0.106067\pi\)
−0.189231 + 0.981933i \(0.560599\pi\)
\(542\) −3.16924 1.82976i −0.00584730 0.00337594i
\(543\) 101.367 175.573i 0.186680 0.323340i
\(544\) −102.817 + 59.3614i −0.189002 + 0.109120i
\(545\) 0 0
\(546\) −23.0634 366.047i −0.0422406 0.670416i
\(547\) 204.209 0.373325 0.186662 0.982424i \(-0.440233\pi\)
0.186662 + 0.982424i \(0.440233\pi\)
\(548\) 86.1706 + 149.252i 0.157246 + 0.272357i
\(549\) −217.321 125.471i −0.395849 0.228544i
\(550\) 0 0
\(551\) −208.024 + 120.103i −0.377539 + 0.217972i
\(552\) 27.3368i 0.0495231i
\(553\) −575.698 + 382.569i −1.04105 + 0.691806i
\(554\) −719.992 −1.29962
\(555\) 0 0
\(556\) −402.706 232.502i −0.724291 0.418169i
\(557\) 268.036 464.253i 0.481214 0.833487i −0.518553 0.855045i \(-0.673529\pi\)
0.999768 + 0.0215578i \(0.00686259\pi\)
\(558\) 24.1861 13.9639i 0.0433443 0.0250249i
\(559\) 743.660i 1.33034i
\(560\) 0 0
\(561\) 273.987 0.488391
\(562\) −148.979 258.039i −0.265087 0.459144i
\(563\) 857.029 + 494.806i 1.52225 + 0.878874i 0.999654 + 0.0262960i \(0.00837123\pi\)
0.522600 + 0.852578i \(0.324962\pi\)
\(564\) 134.492 232.948i 0.238462 0.413028i
\(565\) 0 0
\(566\) 55.8424i 0.0986616i
\(567\) 56.4324 + 28.0068i 0.0995281 + 0.0493948i
\(568\) −192.630 −0.339137
\(569\) −248.330 430.120i −0.436432 0.755922i 0.560979 0.827830i \(-0.310425\pi\)
−0.997411 + 0.0719076i \(0.977091\pi\)
\(570\) 0 0
\(571\) 71.0244 123.018i 0.124386 0.215443i −0.797107 0.603838i \(-0.793637\pi\)
0.921493 + 0.388395i \(0.126971\pi\)
\(572\) −279.251 + 161.226i −0.488201 + 0.281863i
\(573\) 405.841i 0.708274i
\(574\) 279.884 + 421.176i 0.487604 + 0.733757i
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) 328.551 + 189.689i 0.569413 + 0.328751i 0.756915 0.653514i \(-0.226706\pi\)
−0.187502 + 0.982264i \(0.560039\pi\)
\(578\) 107.107 185.515i 0.185307 0.320961i
\(579\) −29.3476 + 16.9438i −0.0506866 + 0.0292639i
\(580\) 0 0
\(581\) −188.240 + 11.8604i −0.323993 + 0.0204137i
\(582\) 9.04185 0.0155358
\(583\) 187.668 + 325.051i 0.321901 + 0.557549i
\(584\) −214.714 123.965i −0.367661 0.212269i
\(585\) 0 0
\(586\) −109.740 + 63.3584i −0.187269 + 0.108120i
\(587\) 234.204i 0.398984i 0.979899 + 0.199492i \(0.0639292\pi\)
−0.979899 + 0.199492i \(0.936071\pi\)
\(588\) −135.185 + 102.650i −0.229906 + 0.174575i
\(589\) 158.654 0.269361
\(590\) 0 0
\(591\) 269.164 + 155.402i 0.455438 + 0.262948i
\(592\) 44.7931 77.5840i 0.0756641 0.131054i
\(593\) 495.838 286.272i 0.836152 0.482753i −0.0198023 0.999804i \(-0.506304\pi\)
0.855954 + 0.517051i \(0.172970\pi\)
\(594\) 55.3869i 0.0932439i
\(595\) 0 0
\(596\) −439.853 −0.738008
\(597\) 221.630 + 383.874i 0.371239 + 0.643006i
\(598\) −146.188 84.4016i −0.244461 0.141140i
\(599\) −46.7105 + 80.9049i −0.0779807 + 0.135067i −0.902379 0.430944i \(-0.858181\pi\)
0.824398 + 0.566011i \(0.191514\pi\)
\(600\) 0 0
\(601\) 167.140i 0.278103i 0.990285 + 0.139051i \(0.0444053\pi\)
−0.990285 + 0.139051i \(0.955595\pi\)
\(602\) 286.643 190.483i 0.476151 0.316417i
\(603\) 199.746 0.331255
\(604\) 260.922 + 451.930i 0.431990 + 0.748229i
\(605\) 0 0
\(606\) 223.686 387.436i 0.369119 0.639333i
\(607\) 796.002 459.572i 1.31137 0.757120i 0.329047 0.944314i \(-0.393273\pi\)
0.982323 + 0.187194i \(0.0599392\pi\)
\(608\) 136.341i 0.224245i
\(609\) 53.7173 108.238i 0.0882058 0.177730i
\(610\) 0 0
\(611\) −830.484 1438.44i −1.35922 2.35424i
\(612\) −109.054 62.9623i −0.178193 0.102880i
\(613\) −389.718 + 675.011i −0.635755 + 1.10116i 0.350600 + 0.936525i \(0.385978\pi\)
−0.986355 + 0.164635i \(0.947356\pi\)
\(614\) −576.215 + 332.678i −0.938462 + 0.541821i
\(615\) 0 0
\(616\) 133.672 + 66.3402i 0.217000 + 0.107695i
\(617\) −510.821 −0.827911 −0.413956 0.910297i \(-0.635853\pi\)
−0.413956 + 0.910297i \(0.635853\pi\)
\(618\) −111.514 193.148i −0.180443 0.312536i
\(619\) −808.792 466.956i −1.30661 0.754372i −0.325082 0.945686i \(-0.605392\pi\)
−0.981529 + 0.191314i \(0.938725\pi\)
\(620\) 0 0
\(621\) 25.1104 14.4975i 0.0404355 0.0233454i
\(622\) 355.390i 0.571367i
\(623\) −53.8862 81.0892i −0.0864947 0.130159i
\(624\) 148.199 0.237498
\(625\) 0 0
\(626\) 475.766 + 274.684i 0.760009 + 0.438792i
\(627\) 157.323 272.491i 0.250914 0.434595i
\(628\) 197.784 114.191i 0.314943 0.181832i
\(629\) 470.047i 0.747292i
\(630\) 0 0
\(631\) −614.861 −0.974423 −0.487212 0.873284i \(-0.661986\pi\)
−0.487212 + 0.873284i \(0.661986\pi\)
\(632\) −139.648 241.877i −0.220962 0.382717i
\(633\) −295.336 170.512i −0.466566 0.269372i
\(634\) −105.627 + 182.952i −0.166605 + 0.288568i
\(635\) 0 0
\(636\) 172.505i 0.271234i
\(637\) 131.557 + 1039.85i 0.206526 + 1.63242i
\(638\) −106.232 −0.166508
\(639\) −102.157 176.942i −0.159871 0.276904i
\(640\) 0 0
\(641\) 94.1724 163.111i 0.146915 0.254464i −0.783171 0.621807i \(-0.786399\pi\)
0.930086 + 0.367343i \(0.119732\pi\)
\(642\) 109.325 63.1189i 0.170288 0.0983161i
\(643\) 23.8831i 0.0371432i −0.999828 0.0185716i \(-0.994088\pi\)
0.999828 0.0185716i \(-0.00591187\pi\)
\(644\) 4.91242 + 77.9667i 0.00762798 + 0.121066i
\(645\) 0 0
\(646\) −357.681 619.521i −0.553685 0.959011i
\(647\) 939.928 + 542.667i 1.45275 + 0.838744i 0.998637 0.0522010i \(-0.0166237\pi\)
0.454111 + 0.890945i \(0.349957\pi\)
\(648\) −12.7279 + 22.0454i −0.0196419 + 0.0340207i
\(649\) −549.735 + 317.390i −0.847049 + 0.489044i
\(650\) 0 0
\(651\) −66.4715 + 44.1724i −0.102107 + 0.0678531i
\(652\) 97.4323 0.149436
\(653\) −317.852 550.536i −0.486756 0.843087i 0.513128 0.858312i \(-0.328487\pi\)
−0.999884 + 0.0152254i \(0.995153\pi\)
\(654\) −81.3767 46.9829i −0.124429 0.0718393i
\(655\) 0 0
\(656\) −176.955 + 102.165i −0.269749 + 0.155740i
\(657\) 262.970i 0.400258i
\(658\) −341.723 + 688.555i −0.519336 + 1.04644i
\(659\) −888.955 −1.34895 −0.674473 0.738300i \(-0.735629\pi\)
−0.674473 + 0.738300i \(0.735629\pi\)
\(660\) 0 0
\(661\) −656.362 378.951i −0.992983 0.573299i −0.0868187 0.996224i \(-0.527670\pi\)
−0.906165 + 0.422925i \(0.861003\pi\)
\(662\) 332.998 576.770i 0.503018 0.871253i
\(663\) −673.402 + 388.789i −1.01569 + 0.586409i
\(664\) 76.2114i 0.114776i
\(665\) 0 0
\(666\) 95.0206 0.142674
\(667\) −27.8063 48.1620i −0.0416886 0.0722068i
\(668\) −85.9316 49.6127i −0.128640 0.0742704i
\(669\) −373.270 + 646.522i −0.557952 + 0.966401i
\(670\) 0 0
\(671\) 630.464i 0.939589i
\(672\) −37.9600 57.1230i −0.0564881 0.0850045i
\(673\) −936.839 −1.39203 −0.696017 0.718026i \(-0.745046\pi\)
−0.696017 + 0.718026i \(0.745046\pi\)
\(674\) 376.519 + 652.150i 0.558634 + 0.967582i
\(675\) 0 0
\(676\) 288.560 499.800i 0.426863 0.739349i
\(677\) −214.062 + 123.589i −0.316192 + 0.182554i −0.649694 0.760196i \(-0.725103\pi\)
0.333502 + 0.942749i \(0.391770\pi\)
\(678\) 486.365i 0.717352i
\(679\) −25.7881 + 1.62482i −0.0379795 + 0.00239296i
\(680\) 0 0
\(681\) −151.637 262.644i −0.222669 0.385673i
\(682\) 60.7652 + 35.0828i 0.0890986 + 0.0514411i
\(683\) −350.887 + 607.755i −0.513744 + 0.889831i 0.486129 + 0.873887i \(0.338409\pi\)
−0.999873 + 0.0159438i \(0.994925\pi\)
\(684\) −125.237 + 72.3057i −0.183095 + 0.105710i
\(685\) 0 0
\(686\) 367.112 317.059i 0.535149 0.462185i
\(687\) −58.1435 −0.0846339
\(688\) 69.5313 + 120.432i 0.101063 + 0.175046i
\(689\) −922.498 532.604i −1.33889 0.773011i
\(690\) 0 0
\(691\) −530.850 + 306.486i −0.768234 + 0.443540i −0.832244 0.554409i \(-0.812944\pi\)
0.0640104 + 0.997949i \(0.479611\pi\)
\(692\) 470.682i 0.680176i
\(693\) 9.95302 + 157.968i 0.0143622 + 0.227948i
\(694\) 635.863 0.916230
\(695\) 0 0
\(696\) 42.2832 + 24.4122i 0.0607518 + 0.0350750i
\(697\) 536.047 928.461i 0.769078 1.33208i
\(698\) −404.993 + 233.823i −0.580220 + 0.334990i
\(699\) 268.318i 0.383860i
\(700\) 0 0
\(701\) 161.307 0.230110 0.115055 0.993359i \(-0.463296\pi\)
0.115055 + 0.993359i \(0.463296\pi\)
\(702\) 78.5942 + 136.129i 0.111958 + 0.193916i
\(703\) 467.480 + 269.900i 0.664979 + 0.383926i
\(704\) −30.1488 + 52.2193i −0.0428250 + 0.0741751i
\(705\) 0 0
\(706\) 383.777i 0.543593i
\(707\) −568.349 + 1145.20i −0.803889 + 1.61980i
\(708\) 291.745 0.412069
\(709\) −285.175 493.938i −0.402222 0.696669i 0.591772 0.806106i \(-0.298429\pi\)
−0.993994 + 0.109436i \(0.965095\pi\)
\(710\) 0 0
\(711\) 148.119 256.549i 0.208325 0.360829i
\(712\) 34.0693 19.6699i 0.0478501 0.0276263i
\(713\) 36.7317i 0.0515171i
\(714\) 322.345 + 159.977i 0.451464 + 0.224057i
\(715\) 0 0
\(716\) 44.2098 + 76.5736i 0.0617455 + 0.106946i
\(717\) −474.887 274.176i −0.662325 0.382393i
\(718\) 5.36270 9.28847i 0.00746894 0.0129366i
\(719\) 431.817 249.310i 0.600580 0.346745i −0.168690 0.985669i \(-0.553954\pi\)
0.769270 + 0.638924i \(0.220620\pi\)
\(720\) 0 0
\(721\) 352.755 + 530.834i 0.489258 + 0.736246i
\(722\) −310.987 −0.430730
\(723\) −202.219 350.254i −0.279695 0.484446i
\(724\) −202.735 117.049i −0.280020 0.161670i
\(725\) 0 0
\(726\) −136.169 + 78.6171i −0.187560 + 0.108288i
\(727\) 1058.79i 1.45638i 0.685375 + 0.728190i \(0.259638\pi\)
−0.685375 + 0.728190i \(0.740362\pi\)
\(728\) −422.675 + 26.6313i −0.580597 + 0.0365815i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) −631.888 364.821i −0.864416 0.499071i
\(732\) −144.881 + 250.941i −0.197925 + 0.342816i
\(733\) −13.1068 + 7.56721i −0.0178810 + 0.0103236i −0.508914 0.860817i \(-0.669953\pi\)
0.491033 + 0.871141i \(0.336620\pi\)
\(734\) 751.530i 1.02388i
\(735\) 0 0
\(736\) −31.5658 −0.0428883
\(737\) 250.922 + 434.609i 0.340463 + 0.589700i
\(738\) −187.690 108.363i −0.254322 0.146833i
\(739\) 81.3819 140.958i 0.110124 0.190741i −0.805696 0.592329i \(-0.798208\pi\)
0.915820 + 0.401588i \(0.131542\pi\)
\(740\) 0 0
\(741\) 892.967i 1.20508i
\(742\) 30.9991 + 491.998i 0.0417778 + 0.663071i
\(743\) −338.071 −0.455009 −0.227504 0.973777i \(-0.573057\pi\)
−0.227504 + 0.973777i \(0.573057\pi\)
\(744\) −16.1241 27.9277i −0.0216722 0.0375373i
\(745\) 0 0
\(746\) −406.564 + 704.189i −0.544991 + 0.943953i
\(747\) 70.0046 40.4172i 0.0937143 0.0541060i
\(748\) 316.373i 0.422959i
\(749\) −300.462 + 199.666i −0.401151 + 0.266577i
\(750\) 0 0
\(751\) −239.087 414.111i −0.318359 0.551413i 0.661787 0.749692i \(-0.269798\pi\)
−0.980146 + 0.198279i \(0.936465\pi\)
\(752\) −268.985 155.299i −0.357693 0.206514i
\(753\) −49.0932 + 85.0319i −0.0651968 + 0.112924i
\(754\) 261.097 150.744i 0.346282 0.199926i
\(755\) 0 0
\(756\) 32.3395 65.1625i 0.0427771 0.0861938i
\(757\) 397.788 0.525479 0.262739 0.964867i \(-0.415374\pi\)
0.262739 + 0.964867i \(0.415374\pi\)
\(758\) −443.684 768.483i −0.585335 1.01383i
\(759\) 63.0874 + 36.4236i 0.0831192 + 0.0479889i
\(760\) 0 0
\(761\) −1264.02 + 729.785i −1.66100 + 0.958981i −0.688767 + 0.724983i \(0.741848\pi\)
−0.972237 + 0.233998i \(0.924819\pi\)
\(762\) 181.540i 0.238241i
\(763\) 240.536 + 119.376i 0.315250 + 0.156456i
\(764\) 468.625 0.613383
\(765\) 0 0
\(766\) −81.5817 47.1012i −0.106503 0.0614898i
\(767\) 900.755 1560.15i 1.17439 2.03410i
\(768\) 24.0000 13.8564i 0.0312500 0.0180422i
\(769\) 2.10093i 0.00273203i −0.999999 0.00136602i \(-0.999565\pi\)
0.999999 0.00136602i \(-0.000434817\pi\)
\(770\) 0 0
\(771\) −503.055 −0.652471
\(772\) 19.5650 + 33.8876i 0.0253433 + 0.0438959i
\(773\) −391.972 226.305i −0.507079 0.292762i 0.224553 0.974462i \(-0.427908\pi\)
−0.731632 + 0.681700i \(0.761241\pi\)
\(774\) −73.7491 + 127.737i −0.0952830 + 0.165035i
\(775\) 0 0
\(776\) 10.4406i 0.0134544i
\(777\) −271.007 + 17.0752i −0.348786 + 0.0219758i
\(778\) 776.473 0.998037
\(779\) −615.594 1066.24i −0.790236 1.36873i
\(780\)